Solve for x
x=6\log_{1.5}\left(10\right)\approx 34.073241524
Solve for x (complex solution)
x=\frac{i\times 2\pi n_{1}}{\ln(1.5)}+6\log_{1.5}\left(10\right)
n_{1}\in \mathrm{Z}
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1.5^{x}=1000000
Use the rules of exponents and logarithms to solve the equation.
\log(1.5^{x})=\log(1000000)
Take the logarithm of both sides of the equation.
x\log(1.5)=\log(1000000)
The logarithm of a number raised to a power is the power times the logarithm of the number.
x=\frac{\log(1000000)}{\log(1.5)}
Divide both sides by \log(1.5).
x=\log_{1.5}\left(1000000\right)
By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
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